Hierarchically ordered patterns

Fig. 10.9 Formation of multiscale structures by combination of the breath figures approach and embossing techniques. The immiscibility between both homopolymers added (PS and PVP) due to the different hydrophilicity produces hierarchical ordered patterns where the PVP is located inside the pore and the PS at the pore wall. In addition, embossing produces an additional level of order at the micrometer length-scale as well as replicas. Reproduced with permission from ref. [205]...

So far, we have discussed various self-assembly and templating mechanisms geared towards the synthesis of porous, ordered materials at different length scales. As was mentioned previously, hierarchically ordered materials that simultaneously exhibit order over all length scales are very attractive novel additions whose synthesis usually requires a combination of all of the techniques mentioned previously. Patterning of mesopores and macropores simultaneously achieves structures with order on several length scales. 

Figure 8 Schematic of the fabrication of hierarchical ordered oxides (a) (Reprinted from Ref. 179, 2001, with permission from Elsevier) scanning electron microscopy (SEM) images (b, c, d), at different magnifications, of hierarchical ordered mesoporons sdica display a high-quality surface pattern ( 1000nm), which is made up of a macroporous ( 100nm) framework of cubic mesoporous silica ( 11 run), as shown in TEM image (e). (Reprinted with permission from P. Yang et al., Science, 1998, 282, 2244)...

Tables 5-13 contain 13C chemical shifts of the coumarin moiety and some other atoms in the molecular backbones of 876 coumarin derivatives. They are arranged according to the substitution patterns and basic molecular systems compiled in Fig. 18 below. Therefore, compound chiffres have been composed in such a way that the basic system (initial letter) and the substitution pattern (numbers after the letter) can be read directly the number after the hyphen indicates the hierarchical order which is given by the nature of that atom in a substituent which is directly connected to the coumarin moiety sequencing according to the Cahn-Ingold-Prelog rule. For example, D348-1 is a trisubstituted coumarin (D) carrying substituents at C-3, C-4 and C-8 (348 3-Br, 4-OH, 8-Me). Since bromine has the top position of all substituents at C-3 in all 3,4,8-trisubstituted coumarins listed, the compounds is the first entry (-1). The only exception from this rule appears in di- and tri-coumarins where the numbers after the letter indicate the positions at which the two (three) coumarin systems are connected.

In many cases it is necessary to synthesize porous materials in a well-defined preordered shape or within confined geometries, which introduces a pathway to fabricate hierarchically ordered porous materials. The techniques mentioned above have been shown to be capable of producing structured and well-ordered templates [61] within capillaries [50], thin plates [62], micromolds [63], or photoresist patterns [64,65]. Spatial adjustment of the surface functionality on the substrate and its wetting properties can yield patterned colloidal films [66,67]. Finally, confining the particle dispersion itself by printing techniques produces micropatterned arrays [68]. This was also shown to work without the necessity of preceding surface patterning steps [69]. 

In order for the network to supply the whole volume of the organism, a hierarchical branching pattern to fill the entire space is required. 

Byun, M., Han, W., Li, B., Xin, X., Lin, Z. An unconventional route to hierarchically ordered block copolymers on a gradient patterned surface through controlled evaporative self-assembly. Angew. Chem. Int. Ed. 52(4), 1122-1127 (2013)... 

Apart from the use of block copolymers providing nanoscale features other methodologies alone or in combination can provide hierarchically stmctured patterns. For instance taking advantage of the template assisted stmcturation, demixing of polymer blend solutions on stmctured substrates can also be employed to create multiscale ordered surfaces. Boneberg et al. [202] employed this approach and blended two components, PVP and PS, already known to form ordered porous films during phase separation [203]. The authors used a micrometer patterned... 

Films formed from blends can also produce hierarchical ordered materials. Raczkowska et al. [66] prepared films from blends of polar PMMA and nonpolar PS. Spin-coating of the blends under an appropriate relative humidity produced macrophase separated domains and simultaneously droplet-like patterns selectively in the domains rich in the polar polymer. Submicrometer pores decorated large PMMA-rich surface regions thus resulting in hierarchical film morphology. 

Figure 18.16 TEM images of star PI-PS-P2VP exhibiting tiling patterns. The arm length ratio is (a) 1 1.08 0.71 (6 ), (b) 1 1.03 1.19 (4.8 ), and (c) 1 1.08 1.92 (4.6.12). (d) 1 2.3 2.0 (314.3.4). ((a)-(c) Reprinted with permission from A. Takano, S. Wada, S. Sato et aL, Observation of cylinder-based microphase-separated structures from ABC star-shaped terpolymers investigated by electron computerized tomography, Macromolecules, 37, 26, 9941-9946, 2004. 2004 American Chemical Society, (d) Reprinted with permission from Y. Matsushita, Creation of hierarchically ordered nanophase structures in block polymers having various competing interactions, Macromolecules, 40, 4, 771-776, 2007. 2007 American Chemical Society.)...

Related experiments yielded the crack patterns shown in Fig. 3. They exhibit a hierarchical order of cracks with even a tendency to regularity though they were grown without making notches into the samples [7]. 

A possibility for the formation of more complex patterns is the use of prepatterned substrates as presented by several authors by either masking the surface partially to avoid the formation of a hard layer in the masked regions [19] or topographical prepatterning, where a relief structure is modified in order to wrinkle [15-17, 34], Periodic porous structures have been reported to undergo pattern transformation due to buckling instabilities when external forces are applied. This results in more complex hierarchical structures [35-37],... 

Another possible application using the hierarchical nature of the wrinkles has been discussed by Efimenko and coworkers [46], They treated a mechanically stretched PDMS sheet with UV-ozone in order to create a stiff surface layer. A detailed analysis with AFM and profilometry of the wrinkles after releasing the strain showed that the wrinkling patterns are hierarchical themselves. They observed up to five generations of different wavelengths with different periodicities. These features made so structured surfaces valuable candidates for separate colloidal particles of different sizes by acting as a micro fluidic sieve. A suspension... 

The data matrix is subjected to hierarchical agglomerative cluster analysis (CA for the mathematical fundamentals see Section 5.3 further presentation of the algorithms is given by [HENRION et al., 1987]) in order to find out whether territorial structures with different multivariate patterns of heavy metals exist within the test area. 

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